8PA 1.2 L8

Pre-Algebra
CRM 1.2 Scientific Notation

Lesson 8
Solving Real-Word Problems
Involving Scientific Notation &
Significant Digits

What are we going to learn today?

CRM 1.2 - Scientific Notation
Lesson 8 - Solving Real-World Problems Involving Numbers Expressed in Scientific Notation

Benchmark(s):
❏

MA.8.NSO.1.6

Learning Target(s):
❏

Solve real-world problems involving operations with numbers expressed in scientific notation.

❏

Express answers in scientific notation using significant digits.

MTR 7 Mathematicians who apply mathematics to real-world contexts:
❏

Connect mathematical concepts to everyday experiences.

❏

Redesign models and methods to improve accuracy or efficiency.

Materials:
❏

⚑Math Nation - Unit 5, Lesson 8 - Volume 1

❏

Calculator

Guided Instruction: Understanding Significant Digits in Scientific Notation

1.

The table shows the distance from Earth, in kilometers (km), to the nearest two planets.

Jackson was asked to find the difference between the two distances and round the distance
to Mars to the nearest whole number so that it was easier to work with.

(6 × 107) − (4 × 107) = (2 × 107)km

Jocelyn was asked to perform the calculation without rounding.

(5.57 × 107) − (3.8 × 107) = (1.77 × 107)km

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Planet

Distance (km)

Scientific Notation

Venus

38 million

3.8 × 107

Mars

55.7 million

5.57 × 107

a.

What is the difference, in km, between the two answers?

b.

Why Jocelyn’s answer is more precise.

PAGE 116

By using significant

figures, we can

show how precise a

number is!

Based on the definition, how many significant digits are in the representations of the
distances for Mars and Venus?

There are three rules for determining how many significant figures are in a number:

PAGE 116

Examples

2027 has 4 significant digits

00052000 has 2 significant digits

00.00800 has 3 significant digits

00035000.0 has 6 significant figures

In

between

zero

Trailing zeros

(in the decimal portion)

Trailing zeros

(NOT in the decimal portion)

Leading zeros

Non-zero digits

●Non-zero digits are always significant.

●Any zeros between two significant digits are significant.

●A final zero or trailing zeros in the decimal portion ONLY are significant.

2.Circle the significant digits in each number. Mark the column(s) to reflect which rule(s) you used when making your
decision.

PAGE 117

Non-Zero

Digits Always

Significant

Zeroes Between
Non-Zero Digits

Always Significant

Zeroes to the

Left of Non-Zero

Digits Not
Significant

All Zeroes to the Right are

Significant if There is a

Decimal Point

# of

Significant

Digits

0.0807

13,401

1,990

5.5

367.0

Sometimes answers written in scientific notation are written using a specific number
of significant digits.

If two numbers are written with different precision, then

The answer’s precision is the least number of significant digits.

Given values of the distance from Earth to Mars and Venus.
Determine how many significant digits should be used to represent
the difference between Mars and Venus.

PAGE 116

The number of
digits that are
meaningful, or
significant, help
mathematicians

and scientists

ensure they have
accuracy in their
measurements.

(5.57 × 107) − (3.8 × 107) = (1.77 × 107)km

Guided Instruction: Using Scientific Notation to Solve Real-World Problems

1.

The National Debt in 2020 was $26.9 trillion. The population for the state of
Florida in 2020 was estimated to be 21.9 million.

If the people living in Florida were to pay off the national debt, how much would
each person pay?

1 Trillion = 10 __

1 Million = 10 __

Math Nation - Unit 3, Lesson 8 - Solving Real-World Problems Involving Numbers Expressed in Scientific Notation - Volume 1, PAGE 118

Your Turn...Are You Ready ?

Math Response

What is the Factor in the answer to this problem

(take into account significant digits)

$$\left(2.450\ x\ 10^{3\ }\right)\ x\ \left(3.36\ x\ 10^5\right)$$

_____ x 10⁸

Type answer here

Correct Answer: 8.23

Deg^°

Rad